Symmetrical lens

ABSTRACT

A family of symmetrical lenses having three components of which the outside two are doublets consisting of an outer biconvex and an inner biconcave lens while the interior lens is biconcave, has been designed primarily for photographic use at substantially unity magnification.

we \I JR OR QTZDQQSB UIInWDsaivwi {LDQJ a Van Orden 1' a March 13, 1973 [54 I SYMMETRICAL LENS 3,044,357 7/1962 Linke .350/202 Inventor: L. Orden, Honey NDY. Buchroedcr et a] [73] Assignee: Busch 8: Lomb Incorporated, P i Ex mi -J hn K, Corbin Rochester, N.Y. Attorney-Frank C. Parker et al. [22] Filed: Feb. 7, 1972 ABSTRACT 4 [211 App] No 22 ,046 A family of symmetrical lenses having three components of which the outside two are doublets consist- [52] [1.5. CI ..350/227, 350/202 ing of an outer bionvex and an inner biconcave lens [5 l I Ill. Cl. ..G02b 9/26, G021) 17/08 while the interior lens is biconcave, has been designed [58] Field of Search ..350/227, 202 primarily for photographic use at substantially unity magnification. [56] References Cited v 54 Claims, No Drawings UNITED STATES PATENTS 7l6,035 l2/l902 Harting ..350/227 SYMMETRICAL LENS BACKGROUND OF THE INVENTION 1. Field of the Invention The field of this invention is lens designs and more specifically those three component designs following a symmetrical positive-negative-positive pattern and having a multiple element exterior component.

2. Description of the Prior Art US. Pat. Nos. 716,035 to C. Harting and 3,301,130 to R. Buchroeder et al. disclose the general shape pattern of the lenses of this invention, however the instant lenses are thought to be operable under conventional conditions at wider relative apertures than those cited.

SUMMARY OF THE INVENTION The lenses of the family disclosed have three components of which the outer two are identical doublets, each having a biconcave lens facing inward and a biconvex lens facing outward. The inner lens is biconcave and is centered between the others. Several specific designs are disclosed herein and all will perform free of distortion, lateral color and coma when used at unit magnification, as is more fully described and set forth in Chapter XIX, Applied Optics 81 Optical Design, A.E. Conrady, Dover, 1960. The other aberrations are sufficiently well corrected for use in unit magnification copying, which is the primary intent of these lenses, although various other uses might be made of them as is well known to those skilled in the optical arts.

The symmetrical lenses disclosed herein may take either a complete form, or may be cut at the center for insertion of a plano mirror so that the lens becomes a retroreflective lens and so that a ray, entering through the front portion, is reflected by the mirror back through the front portion with the same optical effect as though the ray continued on through a complete lens. Obvious economies of material, space and assembly are available from such a configuration.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is an optical diagram illustrating the relative shapes of the lenses arranged in operative position along an optical axis; and

FIG. 2 is an optical diagram similar to FIG. I but cut at the center for use with a plano mirror.

DETAILED DESCRIPTION OF THE INVENTION Since these lenses are symmetrical, those skilledin the art will appreciate that a complete description is obtained from only the first four radii R, the thicknesses t of the elements of the outer doublet and the half-thickness of the inner lens, the space 8 between the outer and inner lenses and the respective glass descriptions, the refractive indices is and the dispersion ratios v.

Thus, the 26 lenses disclosed in the tables below by only those mentioned values are to be understood as being either retroreflective half lenses or as the whole lens, at the option of the reader.

As is conventional in describing lens designs, the drawings show schematic cross-sections of the lenses arrayed in operative positions along an optical axis with the radii, thicknesses and spaces subnumerated in increasing order from one end toward the other. The centers of the radii are taken as positive if on one side and negative if on the other. All radii, thicknesses and spaces are expressed as ratios of the overall focal length so as to facilitate the practice of the invention at any desired focal length. The glass characteristics, the refractive indices m, and the dispersions v, are subnumerated increasingly in the same direction as the other values. It is thought that slight variations in the listed values may be accepted in order to accommodate certain vagaries of manufacture. In particular, the thicknesses t, and t, are thought to be tolerant of at least one unit's variation in the third decimal place and t, to be tolerant of at least a half unit's variation in the third decimal place.

TABLE 1. (Lens design I.)

a. 382] -R, 450] R, 2.025] R 381! l 054] r, 050] lg S, 038] is, 1.678 e,- 1.5 32 n 1.578 v, 55.3 v, 45.9 v, 4 I .5

TABLE 2. (Lens design 2.)

R, .384] R, .424] R, 2.323] -a, .sm t, .054] I, .050) lg .0091 S .054] n, 1 1.697 I! 1.561 I" "i 55.6 v, 45.2 v, 42.3

TABLE 3. (Lens design 3.)

R .386] R, .434! R. 2.4001 R. .382! t .054] r, .050] t .0091 S, .044] is 1.678 In 1.548 I 1.578 r, 55.3 v, 45.7 v, 41.5

TABLE 4. (Lens design 4.)

R .373] Rs .434) R. was; R .38 I r, .050! I] .009] S, .028! a 1.691 in In r, 54.8 's 45.7

TABLE 8. (Lens design 8.)

TABLE 9. (Lens design 9.)

TABLE [0. (Lens design l0.)

TABLE 14. (Lens design 14.)

TABLE 15. (Lent design 15.)

6 TABLE 20. (Lena am. 20.)

TABLE 22. (Lens design 22.)

TABLE 23. (Lens design 23.)

TABLE 25. (Lens design 25.) m 1.678 M 1-1:: ll k, 13% i 1.7211] 45.9 R4 .382] 5 "a 41.5 n .054! :1 38; 3. The lens of claim 1 having values substantially as s' 1035; listed below:

1 .384 :1" if? .424; v, 45.9 2.323f v. 40.9 R4 .372] '1 .054) a .050 a .009 TABLE 26. (Lens design 26.) S. .0541 15 m 1.697 .395] l.56l R, ,45o m- 1.603 R, 2.57s] :1 ii; .375 r 1 .054; 7 i 42.3 g 4. The lens of claim 1 having values substantially as "in 1.697 listed below: n,,, 1.561

:f' if? R1 .3861 v, 45.2 .434; 0 40.9 2.400;

.382] r. .054 I claim: 1, .050) 1. A symmetrical lens having a second half identical g" to its first half and being described by the radii R, 1.... L678 thicknesses t, spaces S and glass types, refractive in- Y dices n and dispersions v subnumerated for the first ,f' 5 half in increasing order from theoutside toward the i 45.7

surface said radii being taken as positive if bent toward the center of said lens, and said radii, thicknesses and spaces being expressed as a ratio of the focal length f and comprising:

an outer doublet having an outer biconvex lens 5. The lens of claim 1 having values substantially as listed below:

defined by the values R R,, 1,, n and v, in sur- 5i face contact with a biconcave lens defined by the R1 l.'l82f values R=, Rs, ts, nm and 1; and 2" :32; an inner singlet lens half of which has a concave sur- '1, .050] face toward said outer doublet, which is separated 8g? l I from each doublet by a space S, and which is a 1,691 defined by the values R., r,, n and 1 said :23: values falling within the ranges given in the table below: 45.7 i 42.3

35; i Eh i 6. The lens of claim 1 having values substantially as 1.473 R. 1498! listed below: 372] 41. .399! 053] i, .055! 049! 1, .051] itl .383! .00s5f 1, .0095] R. .453] .018! s .066] R. 2.229] L678 n, L697 -R4 1 "I 1.532 a 1.561 r, .050] l .5711 1-,, 1.603 r, .0091 54.1; v, 55.6 s .046] 45.2 v, 45.9 n, L678 40,9 v, 42.3 I! 1.532 n L589 2. The lens of claim 1 having values substantially as 2:; listed below:

RI 7. The lens of claim 1 having values substantially as .4501 listed below:

I v 2.025] ll .381] 5 r, 054/ R. 373] g R| 1 .054 a 1; .050; -iz, 1, .0091 R '5 135 s, .0511 il. 3'21 1.61: 1, 1054 n 1.532 1, 050] n 1.603. S 1, 009 v, 55.: s 'o51 v, 45.9 1.61s v, 42.3 n L561 L603 8. The lens of claim 1 having values substantially as listed below: 10 v, 42:3

Rl 13. The lens of claim 1 having values substantial] as Y 24! listed below:

I -R. .3191 1 .054 I5 1; .050; it, 1, .009 a l s. .048] ig 5;? "01 L697 1, '05s; 11,, 1.548 1, 2050] n L578 1, 009) i 55.6 s, '05s! v, r 45.1 1.697 P, 41.5 1| 1.548 1',- L589 9. The lens of claim 1 having values substantially as listed below: 25 v. 4019 h I 14. The lens of claim 1 having values substantially as i I 1'8! hated below: 7' 32*} 1; I050; it, 1. .009! a, '2 774 s .0351 I n 1.69] 1 054 1.54: 'oso 1.51s 1 s' '05s :1 1% m 1.57% .5 ,1, 1.5411 1-,, [.589 10. The lens of claim 1 having values substantially as 5 listed below: v: 40:9

5]. 40 15. The lens of claim I having values substantially as i 1 i389! listed below: R1 .3991 1 .054 1: .050} 5k 1, .009; s. .0351 5' 1.51s 3:2! n 1.54s n L603 f v, 55.3 -32 v, 45.1 I! v, 42.3 1.532 is. 1.603 11. The lens of claim 1 having values substantially as 2:: listed below: v: 42:3

h 5 5 16. The lens of claim 1 having values substantially as a s 1.6! listed below: .3110] :823; 2 a 1, .009] 7! SI ow! 3.131! 1-,, 1.697 '3 n 1.532 Y n 1.51s v 55.6 S. osg 45.9 I in: v, is 1.561 D 6 s n 1.57! 12. The lens of claim 1 having values substantially as z I listed below:

17. The lens of claim 1 having values substantially as listed below:

18. The lens of claim I having values substantially as listed below:

19. The lens of claim 1 having values substantially as listed below:

20. The lens of claim 1 having values substantially as listed below:

21. The lens of claim 1 having values substantially as listed below.

22. The lens of claim 1 having values substantially as listed below:

23. The lens of claim 1 having values substantially as listed below:

24. The lens of claim 1 having values substantially as listed below:

25. The lens of claim 1 having values substantially as listed below:

listed below:

S .035; a, .424 1.091 a. 2.32:; a 1.552 .3111 1.5s9 1 .054; v, 54.: I l. .050] v, 45.9 t .009] v, 40.9 s .0541 M 1.697 27. The lens of claim I having values substantially as fig; listed below: v v,

42.3 R 5:5; 10 0 R, i 2578f 3!. The lens of claim 28 having values substantially R .375] I s m as listed below. a It .386 M1 4. a; n, 1.69 g, 2.400] R [.56l R 382, l 589 54; v, 55 6 050! I! 5 2 h s, .044; "It L678 28. A retroreflective lens having a front doublet comprising: v, 55.3 an outer biconvex lens having radii R and -R,, :1

thickness refractive index n and dispersion w and lying in surface contact with an inner biconcave lens having "Km and R" thickne I, 32. The lens of claim 28 having values substantially refractive index n and dispersion 9,; and v a. below:

a piano-concave lens airspaced from said biconcave R 373 lens of said doublet by a space 8,, having its con- 4 Q cave surface facing said doublet, its plano surface 30 R. 1.782] being reflective, and having a concave radius R 7 3:2; thickness t,, refractive index n and dispersion I: a .050] said radii, thickness and space being expressed in V 32 the table below in ratio to the focal length 1 of said i lens, and radii being taken as negative if centered 35 m- 1.548 on the front side, and all of said values lying within H2 the ranges given in the table below: v, 45.1

.365 R .400 403; '-it, .477; 40 33. The lens of claim 28 having values substantially 4 2 5 2 38; as listed below: 053 t. 049 r oosf r: 0095! h, .018] S 1166! a, I 2.229] 1.678 I, 1.697 -a. 319, L532 is. 1.561 n 05 1.578 I 1.603 05, 54.8 r, .009 45.2 v. 45.9 s n 40.9 V 2.3 a" L613 50 n, 1.552 29. The lens of claim 28 having values substantially 5 as listed below: 1!; 45:9 v, 40.9

R, .3"! v I R, .450! 34. The lens of claim 28 having values substantially 5; 3'2} as listed below:

as; r w a as; s. .oas] R n, 1.67s 4 n L532 t n 1.57s 05! 0, 55.: v, 45.9 a, 1.67% i 1.532 30. The lens of claim 28 having values substantially In 1.605 55 3 as listed below: ,4 v, 42.3

35. The lens of claim 28 having values substantially i as listed below:

R, 32 40. The lens of claim 28 having values substantially '1'" 1 a, 5 as listed below: -R. .519; .054 332 a. I 32:; R, 2.1521 9; "m |-6 i 1 .054]' "m 1.54:: 050 "0. 2 .1 1 1 :i 4511 02;

'l n: 1.54s I ll 36. The lens of claim 28 having values substantially -6 as listed below: 13:;

RI 383/ 41. The lens of claim 28 havin values substantiall R 441] 8 Y L345 as listed below: R. .38lf l .054! 333 a, 1:23; oss 1 2.772 f -a. 377; r I054) "m i' is a .050 2 '4 3 r, .009; s .055; v '5 n, 1.678 n L548 n L589 37. The lens of claim 28 having values substantially v. 55.3 30 v, 45.7 as listed below. y, 0'9

5: 42. The lens of claim 28 having values substantially 2339! as listed below:

as; as r 333 a, 133i} 1, -033f R 1.641! f -a. 385 n L678 t b5! ,1 1050) 3 55.5 40 v; 45.7 02% ll v, 42.3 1.532 I! 1.603 38. The lens of claim 28 havmg values substantially v, 55.6 as listed below: 3::

5 43. The lens of claim 28 having values substantially 1.684] as listed below: R .380] 1, .054] 0 R 83 5 i1. 417; 's'. 1040 R. 3.1311 n, 1.697 R. .3121 1.532 n f is? 2 i :1 15:: r zy l. n 1.56l

"II L578 39. The lens of claim 28 having values substantially v, 55.3 as listed below: 6O

Bi I233; 44. The lens of claim 28 having values substantially 3.l35f as listed below: .381! t, .054] R g I, .050] l .390] I; .0091 -11. .4111 S .05lf R. 1.859] n, 1.678 R. .379! n [.56] I] .0541 a 1.603 I, .050;

1, .009] R, .433] s .048! R, 2.2191 I L697 -R .383] 1.532 1, .054 n 1.5119 1, .050 v, 55.6 1, .009; v, 45.9 s, .045; v, 40.9 11,, 1.691 11,, L561 45. The lens of claim 28 having values substantially gig as listed below: v, 15.:

R .390 4 50. The lens of claim 28 having values substantially R: 3493! as listed below: .374] 22;; 5 R .391] 1, .009! l 5 i1, .430; S .0651 2.460] n [.678 .1 3 2 1.5 1, .054! n 1.589 ,050] 55.3 1, .009 I: S, V .OSZf v, g 40.9 1.691 "DI l.56l 46. The lens of claim 28 having values substantially h g as listed below: v, 45.2 v, 40.9

R .385 25 R, .456; 51. The lens of claim 28 having values substantially R 1.9531 4 38 as llsted below. "323i 1, R .400] .009! -iz, .4541 Sl 039] 2.431] n 1.697 V R ssaf "m .548 I 054, n .603 l: 0501' v 55.6 a 009}- V; 45.7 SI v 5 4213 1.697 "m 1.561 47. The lens of claim 28 having values substantially 3 gig as listed below: 7 v; 45.2 v, 41.5

R .381! -1'z, .419 40 52. The lens of claim 28 having values substantially Ea 3:2} as listed below: 11:11 R .365] s f -i1, .454; S. R4 1 1.473; "m 1.691 .386] 1. .054] u L603 I 050! v, .009 S, .0l8f s n, 1.691 11,, 1.532 48. The lens of claim 28 having values substantially :1- 1.46133 as listed below: ,1 42.3

R .378] R 53. The lens of claim 28 having values substantially "555! as listed below .387) "823} R .381! -iz, .464! 025! R 1 728f "m 1.69] a n 1.532 0 I ,1, 1.578 1 I; 2:23. 3 ggg; "I m 1.691 11,. 1.532 49. The lens of claim 28 having values substantially "no 1. 5:9 as listed below: v, 40.9

54. The: lens of claim 28 having values substantially .009! as listed below: 5. .066] "m 1.697 n 1.56] Rk n 1.589 Ra 2 5 22:; n 1054 '2 .049] i t It I 1: 

1. A symmetrical lens having a second half identical to its first half and being described by the radii R, thicknesses t, spaces S and glass types, refractive indices nD and dispersions Nu subnumerated for the first half in increasing order from the outside toward the surface said radii being taken as positive if bent toward the center of said lens, and said radii, thicknesses and spaces being expressed as a ratio of the focal length f and comprising: an outer doublet having an outer biconvex lens defined by the values R1, -R2, t1, nD1 and Nu 1 in surface contact with a biconcave lens defined by the values -R2, R3, t2, nD2 and Nu 2; and an inner singlet lens half of which has a concave surface toward said outer doublet, which is separated from each doublet by a space S, and which is defined by the values -R4, t3, nD3 and Nu 3, said values falling within the ranges given in the table below: .365f <R1 <.400f .408f <-R2 <.477f 1.473f <R3 <3.498f .372f <-R4 <.399f .053f <t1 <.055f .049f <t2 <.051f .0085f <t3 <.0095f .018f <S <.066f 1.678 <nD1 <1.697 1.532 <nD2 <1.561 1.578 <nD3 <1.603 54.8 < Nu 1 <55.6 45.2 < Nu 2 <45.9 40.9 < Nu 3 <42.3
 1. A symmetrical lens having a second half identical to its first half and being described by the radii R, thicknesses t, spaces S and glass types, refractive indices nD and dispersions Nu subnumerated for the first half in increasing order from the outside toward the surface said radii being taken as positive if bent toward the center of said lens, and said radii, thicknesses and spaces being expressed as a ratio of the focal length f and comprising: an outer doublet having an outer biconvex lens defined by the values R1, -R2, t1, nD1 and Nu 1 in surface contact with a biconcave lens defined by the values -R2, R3, t2, nD2 and Nu 2; and an inner singlet lens half of which has a concave surface toward said outer doublet, which is separated from each doublet by a space S, and which is defined by the values -R4, t3, nD3 and Nu 3, said values falling within the ranges given in the table below: .365f <R1 <.400f .408f <-R2 <.477f 1.473f <R3 <3.498f .372f <-R4 <.399f .053f <t1 <.055f .049f <t2 <.051f .0085f <t3 <.0095f .018f <S <.066f 1.678 <nD1 <1.697 1.532 <nD2 <1.561 1.578 <nD3 <1.603 54.8 < Nu 1 <55.6 45.2 < Nu 2 <45.9 40.9 < Nu 3 <42.3
 2. The lens of claim 1 having values substantially as listed below: R1 .382f -R2 .450f R3 2.025f -R4 .381f t1 .054f t2 .050f t3 .009f S1 .038f nD1 1.678 nD2 1.532 nD3 1.578 Nu 1 55.3 Nu 2 45.9 Nu 3 41.5
 3. The lens of claim 1 having values substantially as listed below: R1 .384f -R2 .424f R3 2.323f -R4 .372f t1 .054f t2 .050f t3 .009f S1 .054f nD1 1.697 nD2 1.561 nD3 1.603 Nu 1 55.6 Nu 2 45.2 Nu 3 42.3
 4. The lens of claim 1 having values substantially as listed below: R1 .386f -R2 .434f R3 2.400f -R4 .382f t1 .054f t2 .050f t3 .009f S1 .044f nD1 1.678 nD2 1.548 nD3 1.578 Nu 1 55.3 Nu 2 45.7 Nu 3 41.5
 5. The lens of claim 1 having values substantially as listed below: R1 .373f -R2 .434f R3 1.782f -R4 .386f t1 .054f t2 .050f t3 .009f S1 .028f nD1 1.691 nD2 1.548 nD3 1.603 Nu 1 54.8 Nu 2 45.7 Nu 3 42.3
 6. The lens of claim 1 having values substantially as listed below: R1 .383f -R2 .453f R3 2.229f -R4 .379f t1 .054f t2 .050f t3 .009f S1 .046f nD1 1.678 nD2 1.532 nD3 1.589 Nu 1 55.3 Nu 2 45.9 Nu 3 40.9
 7. The lens of claim 1 having values substantially as listed below: R1 .373f -R2 .436f R3 1.964f -R4 .384f t1 .054f t2 .050f t3 .009f S1 .031f nD1 1.678 nD2 1.532 nD3 1.603 Nu 1 55.3 Nu 2 45.9 Nu 3 42.3
 8. The lens of claim 1 having values substantially as listed below: R1 .392f -R2 .460f R3 1.964f -R4 .379f t1 .054f t2 .050f t3 .009f S1 .048f nD1 1.697 nD2 1.548 nD3 1.578 Nu 1 55.6 Nu 2 45.7 Nu 3 41.5
 9. The lens of claim 1 having values substantially as listed below: R1 .383f -R2 .441f R3 1.845f -R4 .381f t1 .054f t2 .050f t3 .009f S1 .035f nD1 1.691 nD2 1.548 nD3 1.578 Nu 1 54.8 Nu 2 45.7 Nu 3 41.5
 10. The lens of claim 1 having values substantially as listed below: R1 .381f -R2 .449f R3 2.389f -R4 .399f t1 .054f t2 .050f t3 .009f S1 .033f nD1 1.678 nD2 1.548 nD3 1.603 Nu 1 55.3 Nu 2 45.7 Nu 3 42.3
 11. The lens of claim 1 having values substantially as listed below: R1 .388f -R2 .477f R3 1.684f -R4 .380f t1 .054f t2 .050f t3 .009f S1 .040f nD1 1.697 nD2 1.532 nD3 1.578 Nu 1 55.6 Nu 1 45.9 Nu 3 41.5
 12. The lens of claim 1 having values substantially as listed below: R1 .383f -R2 .408f R3 3.135f -R4 .381f t1 .054f t2 .050f t3 .009f S1 .051f nD1 1.678 nD2 1.561 nD3 1.603 Nu 1 55.3 Nu 2 45.2 Nu 3 42.3
 13. The lens of claim 1 having values substantially as listed below: R1 .393f -R2 .461f R3 2.162f -R4 .378f t1 .054f t2 .050f t3 .009f S1 .055f nD1 1.697 nD2 1.548 nD3 1.589 Nu 1 55.6 Nu 2 45.7 Nu 3 40.9
 14. The lens of claim 1 having values substantially as listed below: R1 .387f -R2 .433f R3 2.772f -R4 .377f t1 .054f t2 .050f t3 .009f S1 .055f nD1 1.678 nD2 1.548 nD3 1.589 Nu 1 55.3 Nu 2 45.7 Nu 3 40.9
 15. The lens of claim 1 having values substantially as listed below: R1 .378f -R2 .471f R3 1.641f -R4 .385f t1 .054f t2 .050f t3 .009f S1 .031f nD1 1.697 nD2 1.532 nD3 1.603 Nu 1 55.6 Nu 2 45.9 Nu 3 42.3
 16. The lens of claim 1 having values substantially as listed below: R1 .391f -R2 .417f R3 3.131f -R4 .376f t1 .054f t2 .050f t3 .009f S1 .059f nD1 1.678 nD2 1.561 nD3 1.578 Nu 1 55.3 Nu 2 45.2 Nu 3 41.5
 17. The lens of claim 1 having values substantially as listed below: R1 .390f -R2 4.77f R3 1.859f -R4 .379f t1 .054f t2 .050f t3 .009f S1 .048f nD1 1.697 nD2 1.532 nD3 1.589 Nu 1 55.6 Nu 2 45.9 Nu 3 40.9
 18. The lens of claim 1 having values substantially as listed below: R1 .390f -R2 .422f R3 3.498f -R4 .374f t1 .054f t2 .049f t3 .009f S1 .065f nD1 1.678 nD2 1.561 nD3 1.589 Nu 1 55.3 Nu 2 45.2 Nu 3 40.9
 19. The lens of claim 1 having values substantially as listed below: R1 .385f -R2 .456f R3 1.953f -R4 .388f t1 .054f t2 .050f t3 .009f S1 .039f nD1 1.697 nD2 1.548 nD3 1.603 Nu 1 55.6 Nu 2 45.7 Nu 3 42.3
 20. The lens of claim 1 having values substantially as listed below: R1 .381f -R2 .419f R3 2.223f -R4 .386f t1 .054f t2 .050f t3 .009f S1 .038f nD1 1.691 nD2 1.561 nD3 1.603 Nu 1 54.8 Nu 2 45.2 Nu 3 42.3
 21. The lens of claim 1 having values substantially as listed below. R1 .378f -R2 .476f R3 1.555f -R4 .387f t1 .054f t2 .050f t3 .009f S1 .025f nD1 1.691 nD2 1.532 nD3 1.578 Nu 1 54.8 Nu 2 45.9 Nu 3 41.5
 22. The lens of claim 1 having values substantially as listed below: R1 .390f -R2 .433f R3 2.219f -R4 .383f t1 .054f t2 .050f t3 .009f S1 .045f nD1 1.691 nD2 1.561 nD3 1.578 Nu 1 54.8 Nu 2 45.2 Nu 3 41.5
 23. The lens of claim 1 having values substantially as listed below: R1 .391f -R2 .436f R3 2.460f -R4 .382f t1 .054f t2 .050f t3 .009f S1 .052f nD1 1.691 nD2 1.561 nD3 1.589 Nu 1 54.8 Nu 2 45.2 Nu 3 40.9
 24. The lens of claim 1 having values substantially as listed below: R1 .400f -R2 .454f R3 2.431f -R4 .383f t1 .054f t2 .050f t3 .009f S1 .058f nD1 1.697 nD2 1.561 nD3 1.578 Nu 1 55.6 Nu 2 45.2 Nu 3 41.5
 25. The lens of claim 1 having values substantially as listed below: R1 .365f -R2 .454f R3 1.473f -R4 .386f t1 .054f t2 .050f t3 .009f S1 .018f nD1 1.691 nD2 1.532 nD3 1.603 Nu 1 54.8 Nu 2 45.9 Nu 3 42.3
 26. The lens of claim 1 having values substantially as listed below: R1 .381f -R2 .464f R3 1.728f -R4 .382f t1 .054f t2 .050f t3 .009f S1 .035f nD1 1.691 nD2 1.532 nD3 1.589 Nu 1 54.8 Nu 2 45.9 Nu 3 40.9
 27. The lens of claim 1 having values substantially as listed below: R1 .395f -R2 .450f R3 2.578f -R4 .375f t1 .054f t2 .049f t3 .009f S1 .066f nD1 1.697 nD2 1.561 nD3 1.589 Nu 1 55.6 Nu 2 45.2 Nu 3 40.0
 28. A retroreflective lens having a front doublet comprising: an outer biconvex lens having radii R1 and -R2, thickness t1, refractive index nD1 and dispersion Nu 1, and lying in surface contact with an inner biconcave lens having radii -R2 and R3, thickness t2, refractive index nD2 and dispersion Nu 2; and a plano-concave lens airspaced from said biconcave lens of said doublet by a space S1, having its concave surface facing said doublet, its plano surface being reflective, and having a concave radius -R4, thickness t3, refractive index nD3 and dispersion Nu 3 said radii, thickness and space being expressed in the table below in ratio to the focal length f of said lens, and radii being taken as negative if centered on the front side, and all of said values lying within the ranges given in the table below: .365f <R1 <.400f .408f <-R2 <.477f 1.473f <R3 <3.498f .372f <-R4 <.399F .053f <t1 <.055f .049f <t2 <.051f .0085f <t3 <.0095f .018f <S <.066f 1.678 <nD1 <1.697 1.532 <nD2 <1.561 1.578 <nD3 <1.603 54.8 < Nu 1 <55.6 45.2 < Nu 2 <45.9 40.9 < Nu 3 <42.3
 29. The lens of claim 28 having values substantially as listed below: R1 .382f -R2 .450f R3 2.025f -R4 .381f t1 .054f t2 .050f t3 .009f S1 .038f nD1 1.678 nD2 1.532 nD3 1.578 Nu 1 55.3 Nu 2 45.9 Nu 3 41.5
 30. The lens of claim 28 having values substantially as listed below: R1 .384f -R2 .424f R3 2.323f -R4 .372f t1 .054f t2 .050f t3 .009f S1 .054f nD1 1.697 nD2 1.561 nD3 1.603 Nu 1 55.6 Nu 2 45.2 Nu 3 42.3
 31. The lens of claim 28 having values substantially as listed below: R1 .386f -R2 .434f R3 2.400f -R4 .382f t1 .054f t2 .050f t3 .009f S1 .044f nD1 1.678 nD2 1.548 nD3 1.578 Nu 1 55.3 Nu 2 45.7 Nu 3 41.5
 32. The lens of claim 28 having values substantially as listed below: R1 .373f -R2 .434f R3 1.782f -R4 .386f t1 .054f t2 .050f t3 .009f S1 .028f nD1 1.691 nD2 1.548 nD3 1.603 Nu 1 54.8 Nu 2 45.7 Nu 3 42.3
 33. The lens of claim 28 having values substantially as listed below: R1 .383f -R2 .453f R3 2.229f -R4 .379f t1 .054f t2 .050f t3 .009f S1 .046f nD1 1.678 nD2 1.532 nD3 1.589 Nu 1 55.3 Nu 2 45.9 Nu 3 40.9
 34. The lens of claim 28 having values substantially as listed below: R1 .373f -R2 .436f R3 1.964f -R4 .384f t1 .054f t2 .050f t2 .009f S1 .031f nD1 1.678 nD2 1.532 nD3 1.603 Nu 1 55.3 Nu 2 45.9 Nu 3 42.3
 35. The lens of claim 28 having values substantially as listed below: R1 .392f -R2 .460f R3 1.964f -R4 .379f t1 .054f t2 .050f t3 .009f S1 .048f nD1 1.697 nD2 1.548 nD3 1.578 Nu 1 55.6 Nu 2 45.7 Nu 3 41.5
 36. The lens of claim 28 having values substantially as listed below: R1 .383f -R2 .441f R3 1.845f -R4 .381f t1 .054f t2 .050f t3 .009f S1 .035f nD1 1.691 nD2 1.548 nD3 1.578 Nu 1 54.8 Nu 2 45.7 Nu 3 41.5
 37. The lens of claim 28 having values substantially as listed below: R1 .381f -R2 .449f R3 2.389f -R4 .399f t1 .054f t2 .050f t3 .009f S1 .033f nD1 1.678 nD2 1.548 nD3 1.603 Nu 1 55.3 Nu 3 45.7 Nu 3 42.3
 38. The lens of claim 28 having values substantially as listed below: R1 .388f -R2 .477f R3 1.684f -R4 .380f t1 .054f t2 .050f t3 .009f S1 .040f nD1 1.697 nD2 1.532 nD3 1.578 Nu 1 55.6 Nu 2 45.9 Nu 3 41.5
 39. The lens of claim 28 having values substantially as listed below: R1 .383f -R2 .408f R3 3.135f -R4 .381f t1 .054f t2 .050f t3 .009f S1 .051f nD1 1.678 nD2 1.561 nD3 1.603 Nu 1 55.3 Nu 2 45.2 Nu 3 42.3
 40. The lens of claim 28 having values substantially as listed below: R1 .393f -R2 .461f R3 2.162f -R4 .378f t1 .054f t2 .050f t3 .009f S1 .055f nD1 1.697 nD2 1.548 nD3 1.589 Nu 1 55.6 Nu 2 45.7 Nu 3 40.9
 41. The lens of claim 28 having values substantially as listed below: R1 .387f -R2 .433f R3 2.772f -R4 .377f t1 .054f t2 .050f t3 .009f S1 .055f nD1 1.678 nD2 1.548 nD3 1.589 Nu 1 55.3 Nu 2 45.7 Nu 3 40.9
 42. The lens of claim 28 having values substantially as listed below: R1 .378f -R2 .471f R3 1.641f -R4 .385f t1 .054f t2 .050f t3 .009f S1 .031f nD1 1.697 nD2 1.532 nD3 1.603 Nu 1 55.6 Nu 2 45.9 Nu 3 42.3
 43. The lens of claim 28 having values substantially as listed below: R1 .391f -R2 .417f R3 3.131f -R4 .376f t1 .054f t2 .050f t3 .009f S1 .059f nD1 1.678 nD2 1.561 nD3 1.578 v1 55.3 Nu 2 45.2 Nu 3 41.5
 44. The lens of claim 28 having Values substantially as listed below: R1 .390f -R2 .477f R3 1.859f -R4 .379f t1 .054f t2 .050f t3 .009f S1 .048f nD1 1.697 nD2 1.532 nD3 1.589 Nu 1 55.6 Nu 2 45.9 Nu 3 40.9
 45. The lens of claim 28 having values substantially as listed below: R1 .390f -R2 .422f R3 3.498f -R4 .374f t1 .054f t2 .049f t3 .009f S1 .065f nD1 1.678 nD2 1.561 nD3 1.589 Nu 1 55.3 Nu 2 45.2 Nu 3 40.9
 46. The lens of claim 28 having values substantially as listed below: R1 .385f -R2 .456f R3 1.953f -R4 .388f t1 .054f t2 .050f t3 .009f S1 039f nD1 1.697 nD2 1.548 nD3 1.603 Nu 1 55.6 Nu 2 45.7 Nu 3 42.3
 47. The lens of claim 28 having values substantially as listed below: R1 .381f -R2 .419f R3 2.223f -R4 .386f t1 .054f t2 .050f t3 .009f S1 .038f nD1 1.691 nD2 1.561 nD3 1.603 Nu 1 54.8 Nu 2 45.2 Nu 3 42.3
 48. The lens of claim 28 having values substantially as listed below: R1 .378f -R2 .476f R3 1.555f -R4 .387f t1 .054f t2 .050f t3 .009f S1 .025f nD1 1.691 nD2 1.532 nD3 1.578 Nu 1 54.8 Nu 2 45.9 Nu 3 41.5
 49. The lens of claim 28 having values substantially as listed below: R1 .390f -R2 .433f R3 2.219f -R4 .383f t1 .054f t2 .050f t3 .009f S1 .045f nD1 1.691 nD2 1.561 nD3 1.578 Nu 1 54.8 Nu 2 45.2 Nu 3 41.5
 50. The lens of claim 28 having values substantially as listed below: R1 .391f -R2 .436f R3 2.460f -R4 .382f t1 .054f t2 .050f t3 .009f S1 .052f nD1 1.691 nD2 1.561 nD3 1.589 Nu 1 54.8 Nu 245.2 Nu 3 40.9
 51. The lens of claim 28 having values substantially as listed below: R1 .400f -R2 .454f R3 2.431f -R4 .383f t1 .054f t2 .050f t3 .009f S1 .058f nD1 1.697 nD2 1.561 nD3 1.578 Nu 1 55.6 Nu 2 45.2 Nu 3 41.5
 52. The lens of claim 28 having values substantially as listed below: R1 .365f -R2 .454f R4 1.473f -R4 .386f t1 .054f t2 .050f t3 .009f S1 .018f nD1 1.691 nD2 1.532 nD3 1.603 Nu 1 54.8 Nu 2 45.9 Nu 3 42.3
 53. The lens of claim 28 having values substantially as listed below: R1 .381f -R2 .464f R3 1.728f -R4 .382f t1 .054f t2 .050f t2 .009f S1 .035f nD1 1.691 nD2 1.532 nD3 1.589 Nu 1 54.8 Nu 2 45.9 Nu 3 40.9 